Search for: All records

The X-cube model, a prototypical gapped fracton model, was shown in Ref. [1] to have a foliation structure. That is, inside the 3+1 D model, there are hidden layers of 2+1 D gapped topological states. A screw dislocation in a 3+1 D lattice can often reveal nontrivial features associated with a layered structure. In this paper, we study the X-cube model on lattices with screw dislocations. In particular, we find that a screw dislocation results in a finite change in the logarithm of the ground state degeneracy of the model. Part of the change can be traced back to the effect of screw dislocations in a simple stack of 2+1 D topological states, hence corroborating the foliation structure in the model. The other part of the change comes from the induced motion of fractons or sub-dimensional excitations along the dislocation, a feature absent in the stack of 2+1D layers. 

Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization. The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories. We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation. Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field. 

Based on several previous examples, we summarize explicitly thegeneral procedure to gauge models with subsystem symmetries, which aresymmetries with generators that have support within a sub-manifold ofthe system. The gauging process can be applied to any local quantummodel on a lattice that is invariant under the subsystem symmetry. Wefocus primarily on simple 3D paramagnetic states with planar symmetries.For these systems, the gauged theory may exhibit foliated fracton orderand we find that the species of symmetry charges in the paramagnetdirectly determine the resulting foliated fracton order. Moreover, wefind that gauging linear subsystem symmetries in 2D or 3D models resultsin a self-duality similar to gauging global symmetries in 1D.